The midfielder's advisor has dismissed reports linking the Germany international with Los Blancos and says he could renew his contract at Signal Iduna Park
Spanish outlet Marca had claimed that the 23-year-old midfielder is set to move to the Santiago Bernabeu for €30 million [£25m].
But Irfan Gundogan has insisted that talks with Dortmund over a new deal have been halted for injury reasons, and not because of an impending transfer to Los Blancos.
"There is no agreement between Gundogan and Real Madrid," the Germany international's dad told Kicker on Friday.
"We only put contract negotiations with Dortmund on hold because we did not want to disturb him during his injury.
"Of course it is still possible that he will renew his contract."
Gundogan is currently sidelined with a persistent back problem but could return to the first team before the end of 2013.